diff --git a/mlir/lib/Dialect/Linalg/Transforms/Tiling.cpp b/mlir/lib/Dialect/Linalg/Transforms/Tiling.cpp
--- a/mlir/lib/Dialect/Linalg/Transforms/Tiling.cpp
+++ b/mlir/lib/Dialect/Linalg/Transforms/Tiling.cpp
@@ -240,10 +240,15 @@
   // Construct (potentially temporary) mins and maxes on which to apply maps
   // that define tile subviews.
   SmallVector<Value, 8> lbs, subViewSizes;
+  AffineMap subviewSizeMap =
+      AffineMap::get(0, 2, {b.getAffineSymbolExpr(0), b.getAffineSymbolExpr(1)},
+                     b.getContext());
   for (unsigned idx = 0, idxIvs = 0, e = tileSizes.size(); idx < e; ++idx) {
     bool isTiled = !isZero(tileSizes[idx]);
     lbs.push_back(isTiled ? ivs[idxIvs++] : (Value)std_constant_index(0));
-    subViewSizes.push_back(isTiled ? tileSizes[idx] : viewSizes[idx]);
+    Value subviewSize =
+        affine_min(subviewSizeMap, ValueRange{tileSizes[idx], viewSizes[idx]});
+    subViewSizes.push_back(isTiled ? subviewSize : viewSizes[idx]);
   }
 
   auto *op = linalgOp.getOperation();